| 研究生: |
黃士沛 Shih-Pei Huang |
|---|---|
| 論文名稱: |
不同決策變數下動態用路人均衡路徑選擇模型之研究 |
| 指導教授: |
陳惠國
Huey-Kuo Chen |
| 口試委員: | |
| 學位類別: |
碩士 Master |
| 系所名稱: |
工學院 - 土木工程學系 Department of Civil Engineering |
| 畢業學年度: | 88 |
| 語文別: | 中文 |
| 論文頁數: | 125 |
| 中文關鍵詞: | 動態用路人均衡路徑選擇 、不動點理論 |
| 外文關鍵詞: | dynamic user-optimal route choice, Fixed Point Theorem |
| 相關次數: | 點閱:8 下載:0 |
| 分享至: |
| 查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
本研究依據Chen and Hsueh (1996)以路段流入率為決策變數所構建之動態用路人均衡路徑選擇模型為基礎,考慮不同問題特性,應用不同決策變數進行動態用路人均衡路徑選擇問題之構建,在此分別就路段流出率與路徑流量兩種不同決策變數進行探討。在以路徑流量為決策變數之動態用路人均衡路徑選擇模型下,本研究除了證明此模型對等於動態用路人均衡條件外,並利用不動點理論(Fixed Point Theorem)進行變分不等式的轉換,以提出此一變分不等式解的存在性證明。
因應不同決策變數模型,本研究提出相對應演算法以進行問題求解,並透過數值例,驗證此模型及演算法的正確性。另外,在以路徑流量為決策變數之動態用路人均衡路徑選擇模型上,分別考慮路段流入率容量限制與路段流出率容量限制的影響,以證實路徑流量模型在動態用路人均衡路徑選擇問題上的適用性。
As follow-up study of Chen and Hsueh (1996) base on link inflow being decision variable to create Dynamic User-Optimal Route Choice Model, this thesis takes into account of figures and applies different decision variables to create dynamic user-optimal route choice problem, discussing by link inflow and route flows. Based on route flows be decision variable, this thesis not only verifies the model be equal to equilibrium conditions but also offers the proof of existence by transferring from Fixed Point Theorem to variational inequality.
To match up different decision variables, this thesis supplies several algorithms and proves its correction with numerical examples. Besides, based on dynamic user-optimal route choice model with route flows being decision variables, it considers individually link inflow capacity and exit flow capacity, to verify the suitability of dynamic user-optimal route choice problem with route flows.
1. 王中允,1999,路段容量限制動態用路人旅運選擇模型之研究,國立中央大學土木工程學系博士論文,中壢。
2. 張美香,1998,動態旅運選擇模型之課題研究,國立中央大學土木工程學系博士論文,中壢。
3. 陳惠國,張美香,1997,「離散型動態用路人最佳化路徑選擇模型之不收斂現象探討」,中華民國第二屆運輸網路研討會論文集,中壢,33-44。
4. 張佳偉,1997,路徑變數產生法求解動態交通量指派模型之效率比較,國立中央大學土木工程學系碩士論文,中壢。
5. 薛哲夫,1996,明確型動態旅運選擇模型之應用,國立中央大學土木工程學系碩士論文,中壢。
6. 陳璐芳,1992,變分不等式在有限空間上的數值方法,國立清華大學應用數學研究所碩士論文,新竹。
7. Bertsekas, D. P., 1976, “On the Goldstein-Levitin-Polyak Gradient Projection Method,” IEEE Transactions on Automatic Control, ac21, 174-184.
8. Border, K. C., 1989, Fixed Point Theorems with Applications to Economics and Game Theory, Cambridge University Press, Cambridge, New York.
9. Chen, H. K. and Chang, M. S., 2000, “Dynamic User-Optimal Departure Time/Route Choice Problem with Time-Window,” Journal of the Chinese Institute of Engineers, 23, 71-81.
10. Chen, H. K. and Wang, C. Y., 1999a, “Dynamic Capacitated User-Optimal Route Choice Problem,” Transportation Research Record 1667, 16-24.
11. Chen, H. K., 1999, Dynamic Travel Choice Models: A Variational Inequality Approach, Springer-Verlag, Berlin.
12. Chen, H. K. and Wang, C. Y., 1999b, “Dynamic User-Optimal Route Choice Problem with First-In-First-Out Requirement,” Journal of Operations Research (Submitted).
13. Florian, M. and Spiess, H., 1982, “The Convergence of Diagonalization Algorithms for Asymmetric Network Equilibrium Problems,” Transportation Research, 16B, 477-483.
14. Friesz, T. L., Bernstein, D. and Stough, R., 1996, “Dynamic Systems, Variational Inequalities and Control Theoretic Models for Predicting Time-Varying Urban Network Flows,” Transportation Science, 30, 14-31.
15. Friesz, T. L., Tobin, R. L. and Wie, B. W., 1994, “The Augmented Lagrangian Method for Solving Dynamic Network Traffic Assignment Models in Discrete Time,” Transportation Science, 28, 204-220.
16. Friesz, T. L., Bernstein, D., Smith, T. E., Tobin, R. L. and Wie, B. W., 1993, “A Variational Inequality Formulation of Dynamic Network User Equilibrium Problem,” Operations Research, 41, 179-191.
17. Friesz, T. L., Luque, F. J., Tobin, R. L. and Wie, B.W., 1989, “Dynamic Network Traffic Assignment Considered as a Continuous Time Optimal Control Problem,” Operations Research, 37, 893-901.
18. Kachroo, P. and Ozbay, K., 1998, “Solution to the User Equilibrium Dynamic Traffic Routing Problem Using Feedback Linearization,” Transportation Research, 32B, 343-360.
19. Karamardian, S., 1974, Fixed Points Algorithms and Applications, Academic Press, Inc., New York.
20. Larsson, T. and Patriksson, M., 1995, “An Augmented Lagrangean Dual Algorithm for Link Capacity Side Constrained Traffic Assignment Problems,” Transportation Research, 29B, 433-455.
21. Nagurney, A., 1993, Network Economics: A Variational Inequality Approach, Kluwer Academic Publishers, Boston.
22. Patriksson, M., 1994, The Traffic Assignment Problem: Models and Methods, Utrecht, The Netherlands.
23. Ran, B. and Boyce, D. E., 1994, Dynamic Urban Transportation Network Models: Theory and Implications for Intelligent Vehicle Highway Systems, Lecture Notes in Economics and Mathematical Systems 417, Springer-Verlag, New York.
24. Ran, B., Rouphail, N. M., Tarko, A. and Boyce, D E., 1997, “Toward a Class of Link Travel Time Functions for Dynamic Assignment Models on Signalized Networks,” Transportation Research, 31B, 277-290.
25. Sheffi, Y., 1984, Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods, Prentice- Hall, Inc., Englewood Cliffs.
26. Singh, S., Watson, B. and Srivastava, P., 1997, Fixed Point Theory and Best Approximation: The KKM-map Principle, Kluwer Academic, Boston.
27. Smith, M. J., 1993, “A New Dynamic Traffic Model and the Existence and Calculation of Dynamic User Equilibria on Congested Capacity-Constrained Road Networks,” Transportation Research, 27B, 49-63.
28. Wie, B. W., Tobin, R. L., Bernstein, D. and Friesz, T. L., 1995, “A Comparison of System Optimum and User Equilibrium Dynamic Traffic Assignments with Schedule Delays,” Transportation Research, 3C, 389-411.
29. Wie, B. W., Tobin, R. L., Bernstein, D. and Friesz, T. L., 1995, “A Discrete Time, Nested Cost Operator Approach to the Dynamic Network User Equilibrium Problem,” Transportation Science, 29, 79-92.
30. Wie, B. W., Tobin, R. L., Bernstein, D., Smith, T. E and Friesz, T. L., 1993, “A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem,” Operations Research, 41, 179-191.
31. Wie, B.W., Friesz, T. L. and Tobin, R. L., 1990, “Dynamic User Optimal Traffic Assignment On Congested Multidestination Networks,” Transportation Research, 24B, 431-442.
32. Wu, J. H., Chen, Y. and Florian, M., 1998, “The Continuous Dynamic Network Loading Problem: A Mathematical Formulation and Solution Method,” Transportation Research, 32B, 173-188.
33. Yang, H. and Qiang, M., 1998, “Departure Time, Route Choice and Congestion Toll in a Queuing Network with Elastic Demand,” Transportation Research, 32B, 247-260.
34. Yao, J. C. and Guo, J. S., 1994, “Variational and Generalized Variational Inequalities with Discontinuous Mappings,” Journal of Mathematical Analysis and Application, 182, 371-392.
35. Yao, J. C. and Guo, J. S., 1994, “Variational Inequalities with Nonmonotone Operators,” Journal of Optimization Theory and Applications, 80, 63-74.